Star Trek: Federation Power Generation

Written: 1998.08.01Last Revised: 1999.02.17

The warp core of a Federation starship (currently off-line).
Plasma conduits can be seen leading to the warp nacelles

Matter/Antimatter Reactors

Fuel Supply

A GCS stores 3000 m³ of antideuterium (TM pg. 68).
Many Federation cultists assume that since deuterium is stored at
13.8K, the antideuterium is also stored at 13.8K. However,
deuterium can be safely stored in physical double-hulled tanks,
while antideuterium must be stored, transported, and processed
entirely in magnetic confinement fields (TM pg. 58, pg. 67). Since
antideuterium atoms are electrically neutral, magnetic-confinement
storage would be extremely difficult. At extreme low
temperatures (<0.002K), the ionic shells of hydrogen atoms
collapse, and the inter-atomic spacing of solid hydrogen can be
calculated based on its atomic radius rather than its ionic radius.
This means that super-cooled anti-deuterium could theoretically be
stored at densities as high as 5600 kg/m³.

However, if it were feasible to cool their
anti-deuterium supply to this sort of extreme low temperature, one
would have to ask why they cannot do this with their deuterium
supply, which is clearlystated in the TM
to be stored in slush form. Cryogenic super-cooling is difficult at
best, particularly when dealing with antimatter. There are three
possible modes of heat energy removal: conduction, convection, and
radiation. Antimatter can only be cooled through one of those three
methods, because the other two methods require direct physical
contact with coolant- obviously not wise when dealing with
antimatter. Even adiabatic demagnetization of paramagnetic crystals
(the 20th century method of super-cooling liquids) is merely a
technique for improving the effectiveness of convection heat energy
removal, rather than a truly new method. Furthermore, the TM states
the following:

"Antimatter,
from the time of its creation, could neither be contained by nor
touch any matter. Numerous schemes were proposed to contain
antihydrogen by magnetic fields. This continues to be the accepted
method. Appreciable amounts of antihydrogen, in the form of liquid,
or better yet, slush, posed significant risks should any portion of
the magnetic containment fail. Within the last fifty years, reliable
superconducting field sustainers and other measures have afforded a
greater degree of safety aboard operational Starfleet vessels."
pg. 67

"Slush
deuterium is created by standard electro-centrifugal fractioning of
a variety of materials, including seawater, outer planet satellite
snows and ices, and cometary nuclei, and chilling down the
fractionated liquid. Each will result in different proportions of
deuterium and tailings, but can be handled by the same Starfleet
hardware. Deuterium tanker craft are far more numerous than their
antimatter counterparts, and can provide emergency reactants on a
few days' notice." pg. 69

Clearly, from the first quote we can determine that they
store it in liquid or slush form. If it were being stored in
solid metallic form at <0.002K, they would list "solid"
or "metallic" as a possible state. Furthermore, if their
starships carried far more antideuterium than deuterium (as
suggested by some Federation cultists), then there would be no
reason for their deuterium tanker fleet to be far larger than their
antimatter tanker fleet as described in the second quote. Therefore,
the storage density of antideuterium aboard a Starfleet vessel is
less than or equal to 160 kg/m³, which is the density of solid
(but not metallic) deuterium. At this density, the ship's 3000 m³
storage tanks should hold roughly 480 tons
of anti-deuterium.

It is confusing why they would use magnetic field
confinement instead of gravimetric confinement, when (as an advanced
space-faring civilization with artificial gravity capability) they
obviously have the technology to confine antimatter with gravity
rather than electromagnetism. Deuterium responds very weakly to
magnetic fields unless it is super-cooled to metallic state, and it
clearly is not, based on the above quotes. However, it is
possible that the TM's description is oversimplified, and overlooks
extra techniques they are using to facilitate the storage of slush
deuterium, such as forcefields, inertial damping (to make it easier
to move the antimatter), or gravimetric suspension. At the very
least, it is likely that they suspend their artificial-gravity net
in the immediate vicinity of the storage tanks so that the volume of
slush needs only an occasional "nudge" to hold it in
place.

Power Output

The theoretical energy density of the matter/antimatter
reaction is 9E16 J/kg, so an upper limit for their energy yield is
roughly 8.6E22 joules (roughly 900 TW average, over three years).
This is more than eighty times as large as the 1E21 joule
energy yield estimated for the total annihilation of the ship's
entire fuel supply in its primary self-destruct sequence (TM pg.
141). The self-destruct sequence occurs in the warp core; the ship
simply dumps its entire matter/antimatter storage into its warp core
at once, so the limited yield of the self-destruct sequence may
suggest poor efficiency for the warp core, perhaps as low as 1.3%
(although Federation cultists are loathe to give up their ridiculous
and unscientific 100% efficiency assumptions). It is possible that
the efficiency of the self-destruct is so low precisely because so
much fuel is being dumped into the warp core at once, but this means
that we can establish that the range of efficiency is somewhere
above 1.3% and somewhere below 100%.

The warp "power" consumption chart in the TM
is useless for determining net power generation for two
reasons:

It uses megajoules as a
unit of power. This is totally incorrect; megajoules are a unit of
energy, not power. Without knowing why they used megajoules
as units (particularly in a fact-checked document as opposed to a
stray spoken word), we cannot determine what time factor should be
applied (naturally, Federation cultists assume that the time factor
is 1/s in the absence of evidence). This may simply be
incompetence; they might have meant "megawatts" but their
scientific knowledge is so poor that they used "megajoules"
instead; of course, this kind of incompetence casts doubt on all
of their figures (spoken or written), but that should not be
surprising from such a primitive society.

The chart measures gross consumption rather than
net output. Since warp nacelles have an output (spatial
distortions) which cannot be measured in terms of watts, it is
impossible to measure their output. The warp chart must
therefore be measuring the gross fuel consumption and converting it
into joules by using the 9E16 J/kg factor. This would explain why
the chart defines power usage instead of power output. This
information is basically a fuel-efficiency chart rather than a
power output chart. For various reasons, the amount of energy that
is actually available to onboard ship systems will be much lower.

Nevertheless, if we insist upon using the chart and
assuming that it refers to megawatts rather than megajoules, then
the power consumption at warp 9.6 would be roughly 3E18 watts. The
TM states that they can maintain this speed for only 12 hours, so
this indicates that their total energy capacity is somewhere in the
area of 1.3E23 joules. This equates to roughly 1440 tons of
matter/antimatter, or 720 tons of antimatter. This is higher than
the 480 tons derived from the storage tank capacity and density
above, but we must remember that the reaction-site temperature is
2E12 K according to the TM, which should be more than enough to
achieve nuclear fusion in the drive plasma. This will obviously
increase the power output of the reaction to beyond what it would be
from matter/antimatter annihilation alone.

Therefore, the peak power output of a GCS is probably in the
range of 1E19 to 1E20 watts, and its average power output is
roughly 900TW. Important: these
figures are based on the energy released at the reaction site
inside the warp core, not the point of actual usage. The
point where the power output is measured is critical to
understanding the wide range of power outputs given by Federation
personnel, as we shall see later. These figures would be consistent
with Data's 1.3E19 watt quantification from "True Q", and
they are also consistent with Geordi Laforge's "terawatt-range"
statement from "Masterpiece Society" and Riker's <1TW
statement from "Dauphin". Does this seem paradoxical? It
should, but it can be explained by noting the context in which
those statements were taken, and the specific location in the
reaction/conversion/usage stage where they were most likely
quantifying their power output (for more details, see the Conflict
Resolution).

Federation Cultist Objections

Many Federation cultists prefer to ignore scientific
issues and the TM in favour of unqualified scraps of dialogue from
Federation crewmembers, but this attitude generally stems from a
combination of scientific ignorance and an absolute refusal to
concede the possibility that Federation crewmembers can ever make
mistakes. Amazingly, they universally maintain this faith in
Federation crewmember infallibility in spite of the long string of
serious scientific and technical mistakes made by Federation
crewmembers over the years:

In "Pegasus",
the supposedly infallible Data believes that the insignificant
gravity of a 10km wide asteroid would cause a violent implosion if
they damaged the asteroid's structure, which would be powerful
enough to destroy their ship. However, the gravity of a 10km wide
asteroid is insignificant. The "infallibility" of Data is
a continually repeated Federation cultist belief that is typical of
their repetitive usage of scientifically ridiculous concepts like
"100% efficiency", "perfect reflectors",
"instant response" etc. All of those concepts defy the
laws of physics, and the concept of a 100% error-free computer
system, no matter how advanced, is just as ludicrous. In fact, the
behaviour of complex systems becomes more unpredictable with
increasing complexity as suggested by mathematical chaos theory,
and this has been demonstrated in Star Trek repeatedly, by the
repeated failures and unexplained acts of their starship computer
systems and holodeck safety interlocks.

In "Cause and
Effect" the supposedly infallible Data mistakenly believes
that their tractor beam will put enough distance between the
Enterprise and the Bozeman to avoid collision, when it will not, as
ensuing events demonstrate.

In "Survivors"
the Enterprise-D's tactical officer quantified energy in units of
gigawatts and megawatts repeatedly.

In "Parallax" they escape a quantum
singularity by finding a "crack" in its event horizon,
even though an event horizon is a mathematically defined radius
from the quantum singularity and therefore cannot possibly have a
"crack", any more than the escape velocity of a planet
has a "crack". This indicates that they do not understand
the concept of an event horizon and that they may not have been
anywhere near a quantum singularity at all, but rather, an entirely
different phenomenon which they mistook for a quantum singularity
in their incompetence.

This is only a small sampling of the serious technical
and scientific mistakes made by high-ranking Federation bridge
officers, yet Federation cultists continue to insist that any
vague dialogue from these characters be treated as more
reliable than science and technical analysis of established
phenomena! Even Federation technical literature is prone to
embarassing scientific errors- the Star Trek Encyclopedia describes
neutrinos as "massless particles" when in fact they are
known to have mass, and their velocity was established to be <c
long before the publication of this Encyclopedia!

"The fuel supplies for the IPS
are contained within the primary deuterium tank (PDT) in the Battle
Section and a set of thirty-two auxiliary cryo tanks in the Saucer
Module. While the PDT, which also feeds the WPS, is normally loaded
with slush deuterium at a temperature of 13.8K, the cryo reactants
stored within the Saucer Module tanks are in liquid form. In the
event that slush deuterium must be transferred from the main tank,
it is passed through a set of heaters to raise the temperature
sufficiently to allow proper fuel flow with minimal turbulence and
vibration."

A GCS stores 62,500 m³ of deuterium, which is stored at
13.8K, in liquid form (TM pg. 69). The average deuterium density
should therefore be roughly 160 kg/m³, for a total mass of
10,000 metric tons of deuterium.
This represents the fusion reactor fuel supply which the Federation
expects to be necessary for a three-year mission period. However,
this figure is based on an assumption of 160 kg/m³ density for
the ship's entire fuel supply. The average density is somewhat
lower. On pg. 75 of the TM, it states:

"The interval volume of each auxiliary tank is 113
cubic metres and each is capable of storing a total of 9.3 metric
tonnes of liquid deuterium."

This quote seems to suggest that the density of liquid deuterium
in the Saucer Module storage tanks is a mere 82 kg/m³, which is
roughly half the density of liquid deuterium. In fact, this
is the density of liquid hydrogen, not liquid deuterium. We can only
postulate that these tanks cannot be filled to capacity, and that
roughly half of their internal volume is actually low-pressure
deuterium vapour. It is possible that structural limitations
keep them from filling their tanks to full capacity, or perhaps
there are other extenuating factors involving safety concerns. In
any case, it would appear that the total fuel capacity of a GCS is
less than or equal to 10,000 tons.

A typical isotopic hydrogen fusion reaction yields roughly 20 MeV
to 30 MeV of energy, depending on the type of reaction. However, the
"coulomb barrier" for this type of fusion is roughly
200 keV, which means that deuterons must have ~200 keV of kinetic
energy to overcome mutual magnetic repulsion and come into contact.
Also, two neutrinos are generally produced in each cycle, and this
costs roughly 500 keV of energy. Therefore, the theoretical upper
limit for net energy production from the fusion of two deuterium
atoms is 26 MeV. There are roughly 3E26 deuterium atoms in a
kilogram, so this works out to roughly 6.2E14 J/kg. This is a highly
unrealistic estimate however, since it assumes that all of the atoms
will be grouped into pairs that are headed directly for one another!

In real life, temperatures and pressure vastly in excess of the
theoretical minimum are necessary to induce fusion. Even when those
temperatures and pressures are present, only a small percentage of
the deuterium atoms will actually react. Even in the core of a
G-class star, less than 1 in 40,000 deuteron-deuteron encounters
will result in fusion. In fact, the extremely low probability of
deuteron-deuteron encounters regulates the rate of reaction and is
the sole reason that stars exist for as long as they do, rather than
exploding. Compounding the problem is the fact that their impulse
drive hurls a substantial portion of its fuel into space as
propellant, still in hydrogen plasma state (as seen in ST6).
Obviously, this means that a very large proportion of the impulse
engine's fuel does not react, as postulated above. What does this
mean? It means that we cannot make a reasonable determination of
fusion reactor output simply by looking at their fuel supply.

So how do we determine the power output of a GCS fusion
reactor? There are a few possibilities:

Some Federation cultists attempt
to use the instantaneous power figures from the TM to generate
unrealistically high power estimates for starship fusion reactors,
because it states that the peak instantaneous power during each
pellet detonation is 1E11 MW. However, they are ignoring the DS9 TM
as well as the distinction between instantaneous and average power.
The instantaneous power only describes the peak power during the
microsecond that their laser fusion initiators strike each pellet.
This information is useless without knowing the number of pellets
launched into the reactor per unit time, because the power curve in
a pellet-type fusion reactor will be at zero most of the time, and
spike to a peak during each pellet reaction. The height of this
peak in no way defines the average power output, although it could
be used to generate an extremely high upper limit. This upper limit
will not be very useful, because of the extreme swings in power
output experienced by a pellet-type reactor.

The DS9 TM states that the total
power output of DS9's fusion reactors is 790
TW, therefore we can estimate that the fusion reactors
of a GCS are much less powerful than 790 TW. Otherwise, it would be
difficult to explain how DS9 easily held off entire fleets
of starships in Way of the Warrior and A Call to Arms.
Those starships had access to fusion power from their impulse
drives, as well as warp power (warp cores can produce shared power
for ship's systems even when at sublight speeds). It would
therefore seem reasonable to suggest that a typical starship's
fusion reactor is much less powerful than 790 TW.

According to the warp power chart on page 55 of the TNG TM,
the power requirement for achieving warp 1 is approximately 2E4
"megajoules/cochrane", dropping to 2E2
"megajoules/cochrane" just after achieving warp 1 (the
energy requirement for crossing the threshold is much higher than
the energy requirement once the ship has entered warp).
Furthermore, we know that warp 1 is precisely 1 cochrane. If we use
the almost universal Federation cultist assumption that the units
of megajoules are actually an error, and should be megawatts,
then this means that the power requirement for achieving warp 1 is
approximately 20 GW, and the power requirement for maintaining
warp 1 is approximately 200 MW. 20 GW
is therefore the upper limit for GCS fusion reactor output, since a
GCS fusion reactor is not powerful enough to achieve warp speed.
This is the reason that starships are limited to impulse speeds
when their warp cores have either run out of antimatter fuel,
become damaged, or been ejected for safety reasons.

Although the inability of an impulse drive to propel a starship
to warp speeds is generally accepted, some Federation cultists would
undoubtedly object to the logic used to derive the 20GW figure
above. Therefore, they will undoubtedly require the usual repetitive
evidence before they accept the figure:

"The M/ARA is the principal power-generating system
because of the 1E6 greater energy output of the matter/antimatter
reaction over that of standard fusion, as found in the impulse
propulsion system" pg. 57

"The multimode sustainer engine is not a true warp
engine due to its small physical size, one twelfth the minimum
matter/antimatter (M/A) reaction chamber size." pg. 129

It is quite clear that a warp core is required to achieve warp
speeds. Even Zefram Cochrane's original warpship, the Phoenix, had a
warp core. Therefore, since we know that starship fusion reactors
cannot generate enough power to achieve warp speeds, they must be
limited to 20GW or less. This makes sense, since an entire fleet of
starships was unable to overwhelm DS9 even though DS9 is powered by
a 790TW fusion reactor group and the starships were using both their
fusion reactors and warp cores to supply power.

Space Station Power Generation

The DS9 TM clearly described the power output of DS9, which
is one of the largest and most prominent space stations in the
Federation:

"the reaction chamber group is the heart of the
generator, potentially capable of producing 790 terawatts of power
with all six chambers running."

Since DS9 was able to hold its own against entire fleets
of enemy starships in Way of the Warrior and A Call to
Arms, we can conclude that its power is at least average
for a Federation space station.

Some Federation cultists question why DS9 does not use
matter/antimatter reactors, but this is a ludicrous question. On pg.
67, the TM states: "Antimatter is first generated at major
Starfleet fueling facilities by combined solar-fusion charge
reversal devices ... there is a net energy loss of 24% using this
process". In the discussion of its onboard antimatter
generation system, it goes on to state: "the law of
conservation of energy dictates that the power required for this
process will exceed the usable energy ultimately derived from the
resulting antimatter fuel" on pg. 72.

In other words, for every kilogram of antimatter stored on a
Federation starship, at least 1.8E17 joules of energy were
generated in fusion reactors, somewhere in Federation space, to
produce it. Another way of putting this is that at least half
of the Federation's total power-generation capacity, including both
starships and starbases, must be fusion-based. Otherwise,
they would not be producing enough antimatter to meet demand.

Therefore, all Federation starbases probably use fusion for their
power source. Matter/antimatter is a net-loss system since
each kilogram of antimatter will cost at least 1.8E17 joules to
produce, and will generate less than 1.8E17 joules when it is
annihilated with an equal amount of matter. Fusion is a net-gain
system since fusion fuels can be harvested from natural sources.
Therefore, the requirements of starship antimatter consumption
dictate that the Federation must use net-gain power sources such as
fusion, in their starbases and refueling installations.

When we contrast the 790TW of a large Federation space station
with the 1E33 watts generated by the Death Star's hypermatter
reactor, we can see that it would take more than forty years
for one billion DS9 space stations to generate the energy
that the Death Star generates in one second! Obviously, the
Federation lags so far behind us in power generation technology that
there is little point even bothering to perform direct comparisons
like this one- the disparity is too large.

Conclusion

Star Trek Federation power generation technology is extremely
limited. None of their battlestations are mobile, their starship
power generation systems are extremely inefficient, and even the
most optimistic quantifications of their power generation systems
indicate that their power output is less than 1% of a Star
Destroyer's power output. Even a heavily-armed space station like
DS9 is limited to terawatt-range power generation, based on
deuterium fusion. Starships are limited to mere gigawatt-range
power output! They have been unable to produce planetary shields or
move planets as we have, and their crewmembers appear to have very
poor scientific knowledge (based on their repeated mistakes).

Acknowledgements

Brian Young, for pointing out DS9 TM quantification of
fusion reactor power output.